2025/02/12 by Yeow Meng Chee, Chee, Yeow Meng, Tuvi Etzion +5
Computer Science · Engineering · #Cellular Automata and Applications #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2502.08424
openalex publication_date 2025/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An (n,R)-covering sequence is a cyclic sequence whose consecutive n-tuples form a code of length n and covering radius R. Using several construction methods improvements of the upper bounds on the length of such sequences for n ≤ 20 and 1 ≤ R ≤ 3, are obtained. The definition is generalized in two directions. An (n,m,R)-covering sequence code is a set of cyclic sequences of length m whose consecutive n-tuples form a code of length~n and covering radius R. The definition is also generalized to arrays in which the m × n sub-matrices form a covering code with covering radius R. We prove that asymptotically there are covering sequences that attain the sphere-covering bound up to a constant factor.